报告人：Prof. Xiang Zhou（City University of Hong Kong）
地点：精正楼306
摘要：Fokker-Planck equation (FPE) is the time evolution (linear) partial differential equation (PDE) for the density function of a diffusion process associated with an Ito stochastic differential equation (SDE). It is the diffusion version of the master equation for Markov processes. Despite of its simple linear form, FPE is an important alternative tool for the stochastic dynamical systems to understand phenomena from equilibrium to nonequilibrium cases and it drives any distribution to its own stationary distribution. FPE is also a gradient dynamics in the probability space equipped with Wasserstein metric. It is closely connected to the sampling problem in Monte Carlo method, the stochastic optimization algorithms and generative modelling in machine learning. This series of lectures will introduce the basics of FPE for advanced undergraduate students and review the FPE-related topics from aspects of analysis, computation and applications, by trying to build the connections across different applications and with special attention to irreversible situations. Recent works of using SDE and FPE in machine learning literature will also be briefly commented in these lectures.
The twenty lectures topics are:
(1) Foundations: Markov process;
(2) stochastic differential equation;
(3) Kolmogorov equation; generator;
(4) entropy; information theory;
(5) Fokker Planck equation for reversible SDE:
(6) potential;
(7) detailed balance; Boltzmann-Gibbs distribution;
(8) self-adjoint generator; time reverse;
(9) Fokker Planck equation for irreversible SDE:
(10) ergodicity;
(11) decomposition of forces;
(12) entropy;
(13) Energy dissipation of Fokker Planck equation:
(14) Lyapunov functional and free energy;
(15) exponentially decay;
(16) (log-)sobolev inequality;
(17) Gradient flow in probability space；
(18) Fokker Planck equation;
(19) Wasserstein flow;
(20) JKO splitting
时间：
10/20, Wednesday, 1:30to 2:20 pm
10/20, Wednesday, 2:30to 3:20 pm
10/22, Friday, 1:30to 2:20 pm
10/22, Friday, 2:30to 3:20 pm
10/25, Monday, 1:30to 2:20 pm
10/25, Monday, 2:30to 3:20 pm
10/27, Wednesday, 1:30to 2:20 pm
10/27, Wednesday, 2:30to 3:20 pm
10/29, Friday, 1:30to 2:20 pm
10/29, Friday, 2:30to 3:20 pm
11/1, Monday, 1:30to 2:20 pm
11/1, Monday, 2:30to 3:20 pm
11/3, Wednesday, 1:30to 2:20 pm
11/3, Wednesday, 2:30to 3:20 pm
11/5, Friday, 1:30to 2:20 pm
11/5, Friday, 2:30to 3:20 pm
11/8, Monday, 1:30to 2:20 pm
11/8, Monday, 2:30to 3:20 pm
11/10, Wednesday, 1:30to 2:20 pm
11/10, Wednesday, 2:30to 3:20 pm
联系人：孙志伟、陈景润